Q #1

12. [0.5/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Given x, and x, distributions that are normal or approximately normal with unknown of and 2, the value of t corresponding to x1 - X2 has a distribution that is approximated by a Student's t distribution. We use the convention that the degrees of freedom is approximately the smaller of n, - 1 and n2 - 1. However, a more accurate estimate for the appropriate degrees of freedom is given by Satterthwaite's formula: d.f. ~ + 7 2 - 1 ( 2 ) where S,, 52, my, and n, are the respective sample standard deviations and sample sizes of independent random samples from the x, and x, distributions. This is the approximation used by most statistical software. When both n, and n2 are 5 or larger, it is quite accurate. The degrees of freedom computed from this formula are either truncated or not rounded. (a) We tested whether the population average crime rate u, in the Rocky Mountain region is higher than that in New England, u, . The data were n, = 15, x, ~ 3.51, s, ~ 0.91, n2 = 12, x2 2 3.87, and 52 2 0.97. Use Satterthwaite's formula to compute the degrees of freedom for the Student's t distribution. (Round your answer to two decimal places.) d.f. =13. [0.75/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.028.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if , and 2 are unknown but we have reason to believe that o 1 = 02, we can pool the standard deviations. Using sample sizes n, and n2, the sample test statistic x, - x, has a Student's t distribution where * 1 - x 2 t = with degrees of freedom d.f. = n1 + n2 - 2 SV ny and where the pooled standard deviation s is S = 1 (n1 - 1)s12 + (12 - 1) 522 n1+ 12 - 2 Note: With statistical software, select the pooled variance or equal variance options. LA USE SALT (a) There are many situations in which we want to compare means from populations having standard deviations that are equal. This method applies even if the standard deviations are known to be only approximately equal. Consider a report regarding average incidence of fox rabies in two regions. For region I, n, = 16, x] ~ 4.75, and s, = 2.82 and for region II, n2 = 15, X2 P2 O Ho: P1 = P2i H1: P1 = P2 O Ho: P1 = P2; H1: P1 * P2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. The number of trials is sufficiently large. O The Student's t. The number of trials is sufficiently large. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. We assume the population distributions are approximately normal. What is the value of the sample test statistic? (Test the difference P, - P2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)15. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.5.036. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 11 children (9 years old) showed that they had an average REM sleep time of x1 = 2.9 hours per night. From previous studies, it is known that of = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of X2 = 2.40 hours per night. Previous studies show that 2 = 0.8 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 5% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference , - M2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value P-value8. [0.78/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 8.R.009.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensive burn patients was about 60%. Using the new compresses, the hospital found that only 42 of 91 patients with extensive burns died. Use a 1% level of significance to test the claim that the mortality rate has dropped. LA USE SALT What are we testing in this problem? O single mean single proportion (a) What is the level of significance? 0.60 X